Difference frequency imaging and spectroscopy to measure dopants using an alternating current scanning tunneling microscope

ABSTRACT

A tunable high frequency AC scanning tunneling microscope (ACSTM) has been utilized to image and to record spectra for semiconductor characterization. A difference frequency mixing technique sensitive to dopant type and concentration is applied both to uniformly doped and to patterned semiconductor substrates. Uniformly doped silicon substrates were used to characterize the difference frequency spectral signature for both p- and n-type Si. Comparison of the measured difference frequency to such signature can be used for distinguishing between the two types of dopants in samples with unknown dopant type. Patterned substrates were then fabricated, and a spectroscopic imaging mode was used to map out dopant density at ultrahigh resolution, and to distinguish between areas of different concentration and different dopant type. By measuring samples of known dopant dosages to form a reference database, the unknown dosage of the same dopant in a portion of a sample may be found by comparing the difference signal measured from the sample to the reference database.

[0001] This work was supported by the US Department of Commerce/NOAAContract #50DKNB990085; the government has rights to the invention inthis application.

BACKGROUND OF THE INVENTION

[0002] This invention relates in general to systems for measuringdopants, and in particular a system using difference frequency imagingand spectroscopy to measure dopants or other atomic characteristicsusing an alternating current scanning tunneling microscope (“ACSTM”).

[0003] Scanning probe microscopes are extremely important forcharacterizing semiconductors with very high spatial resolution.According to the 1999 International Technology Roadmap forSemiconductors (1), there was already an unmet critical need to be ableto determine 2-D dopant profiles with 3 nm resolution in 1999, and 1 nmspatial resolution will be needed by 2008. Much of the recent work inthis field has focused on the development of the scanning capacitancemicroscope (SCM). See, for example:

[0004] (1) Capacitance-Voltage Measurement and Modeling on a NanometerScale by Scanning C-V Microscopy, by Y Huang and C. C. Williams; Journalof Vacuum Science and Technology B 12, 369 (1994)

[0005] (2) Quantitative Two-Dimensional Dopant Profile Measurement andInverse Modeling by Scanning Capacitance Microscopy by Y Huang, C. C.Williams, and J. Slinkman; Applied Physics Letters 66, 344 (1995)

[0006] (3) Scanning Capacitance Microscopy and Spectroscopy Applied toLocal Charge Modifications and Characterization of Nitride-Oxide-SiliconHeterostructures by M. Dreyer and R. Wiesendanger; Applied Physics A 61,357 (1995)

[0007] (4) Scanning Capacitance Microscopy Measurements and Modeling:Progress Towards Dopant Profiling of Silicon, by J. J. Kopanski, J. F.Marchiando, and J. R. Lowney; Journal of Vacuum Science and Technology B14, 242 (1996)

[0008] (5) Contrast Reversal in Scanning Capacitance Microscopy Imaging,by R. Stephenson, A. Verhulst, P. DeWolf, M. Caymax, and W. Vandervorst;Applied Physics Letters 73, 2597 (1998)

[0009] (6) Scanning Capacitance Microscope Methodology for QuantitativeAnalysis of p-n Junctions, by V. V. Zavyalov, J. S. McMurray, and C. C.Williams; Journal of Applied Physics 85, 7774 (1999)

[0010] (7) pn-Junction Delineation in Si Devices Using ScanningCapacitance Spectroscopy, by H. Edwards, V. A. Ukraintsev, R. SanMartin, F. S. Johnson, P. Menz, S. Walsh, S. Ashburn, K. S. Wills, K.Harvey, and M.-C. Chang; Journal of Applied Physics 87, 1485 (2000)

[0011] These instruments have shown high sensitivity towards dopantdensity and type, and have accurately imaged devices on semiconductorsurfaces with resolution as high as 10 nm. However, the lateralresolution when using capacitance detection is limited by the probe tipgeometry and dopant level. Improving spatial resolution requires thedevelopment of new scanning probe techniques.

[0012] As one type of scanning capacitance microscope, a two-frequencymixing strategy designed to image p-n junctions using a microwavefrequency compatible atomic force microscope (AFM) has been reported byJ. Schmidt, D. H. Rapoport, G. Behme, and H. -J. Frohlich, J. Appl.Phys., 86, 7094 (1999). These particular AFM experiments used the sumand third harmonic frequencies as nonlinear mixing product signals. Itwas found that the sum frequency signal and the third harmonic signalare proportional to dC/dV and d²C/dV², respectively, where C is thecapacitance and V the voltage across the AFM tip and the sample.

[0013] None of the above systems is entirely satisfactory. It istherefore desirable to provide an instrument for measuring dopants withimproved capabilities.

SUMMARY OF THE INVENTION

[0014] This invention is based on the observation that theabove-described mixing strategy reported by J. Schmidt referenced abovecan be improved as follows. By measuring at a frequency substantiallyequal to the difference between the frequencies of two alternatingcurrent (AC) signals, or a multiple thereof, applied to a dopedsemiconductor material, it is possible for dopants to be detected at amuch lower frequency than the frequencies of the AC signals applied. Asused here-in-below, the term “difference frequency” refers to thedifference between the frequencies of two alternating current (AC)signals, or a multiple thereof. This has the advantage of detectingsignals at frequencies much below the microwave range so that thedetection instrument can be much simplified compared to that employed byJ. Schmidt referenced above.

[0015] Applicants discovered that the signal measured at the differencefrequency depends upon the magnitude of the direct current (DC) biasvoltage applied between the STM tip and the sample. Thus, preferably,the DC bias voltage is varied to optimize the difference frequencysignal that is to be detected before the sample is measured at such DCbias voltage. For some applications, this means tuning the DC biasvoltage until the amplitude of the difference frequency signals is at amaximum. For other applications, this may mean tuning the DC biasvoltage until the best contrast is achieved between the measurement oftwo types of dopants. Still other optimization schemes are possible.

[0016] Applicants recognized that the difference frequency signal alsodepends upon the frequencies of the two or more AC signals applied tothe sample. In other words, such amplitudes can be optimized by tuningthe frequencies of the two or more AC signals applied to the sample.Therefore, preferably, the frequencies of the two or more AC signalsapplied to the sample can be swept in frequency either upwards ordownwards until the amplitude of the difference frequency signal isoptimized in one of a variety of ways as described herein.

BRIEF DESCRIPTION OF THE FIGURES

[0017]FIG. 1 is a partly schematic and partly cross-sectional view of aportion of an ACSTM and a positioning mechanism for positioning a samplerelative to the probe tip of the ACSTM to illustrate the invention.

[0018]FIG. 2A is a block diagram of the ACSTM of FIG. 1 illustrating anembodiment of the invention that detects at a difference frequency toillustrate an embodiment of the invention.

[0019]FIG. 2B is a block diagram of a portion of the ACSTM of FIG. 2Aillustrating a mechanism for causing relative motions between the probetip and the sample so that the sample may be scanned to provide aprofile of dopants or other atomic characteristics of the sample toillustrate an embodiment of the invention.

[0020]FIGS. 3A, 3B are graphical plots of difference frequency signalamplitudes for p- and n-type doped silicon as a function of fundamentalmodulation frequencies and DC bias values to illustrate the invention.

[0021]FIG. 4A is a graphical plot of model capacitance curves of ametal-insulator-semiconductor structure for both p- and n-typesemiconductors to illustrate the invention.

[0022]FIG. 4B is a graphical plot of dC/dV curves corresponding to thosein FIG. 4A, determined numerically based on the capacitance curves inFIG. 4A to illustrate the invention.

[0023] FIGS. 5A-5D are difference frequency signal images of aphosphorus-doped silicon substrate with boron implant stripes at variousDC biases to illustrate the invention.

[0024]FIG. 6 is a difference frequency signal image of a p-type siliconsubstrate doped with stripes of boron to illustrate the invention.

[0025]FIG. 7 is a graphical plot of the relationship between differencefrequency signal amplitude and resistivity of doped semiconductormaterials, showing that difference frequency signal amplitude variesdirectly and monotonically with resistivity of doped semiconductormaterials.

[0026]FIG. 8A is a topograhical image of a doped semiconductor sample,and FIG. 8B is a profile of the sample obtained using the invention ofthe difference frequency signal amplitude.

[0027] For simplicity in description, identical components areidentified by the same numerals in this application.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] To address these and related issues, the applicants havedeveloped a novel dopant profiling tool based on the alternating currentscanning tunneling microscope (ACSTM). The STM is a well-establishedsurface probe that is routinely capable of spatial resolution on theatomic scale. The applicants' goal has been to incorporate theunparalleled imaging capability of the STM with an accurate dopantprofiling system. The instrument is based on a custom-built alternatingcurrent scanning tunneling microscope (ACSTM), such as those describedin: S. J. Stranick and P. S. Weiss, Rev. Sci. Instrum., 64, 1232 (1993);S. J. Stranick and P S. Weiss, Rev. Sci. Instrum., 65, 918 (1994) and L.A. Bumm and P. S. Weiss, Rev. Sci. Instrum., 66, 4140 (1995).

[0029] The instrument was adapted in several ways to facilitate dopantprofiling. The ability to position the sample in three dimensions withsub-micron resolution is desirable to locate devices on or beneath asurface, so that they can be imaged with the ACSTM. In order toaccomplish this, a beetle-style microscope was designed and built (shownschematically in FIG. 1). The new ACSTM was based on the design ofprevious ACTSMs, described in the three references above by Stranick andBumm et al. It was built to have a relatively large scan range,approximately 15 microns, increasing the area that can be investigatedduring a single image by over two orders of magnitude compared toearlier ACSTM designs. A similar design is described in U.S. Pat. No.5,559,328, which is incorporated herein in its entirety by reference.

[0030] The instrument is also equipped with a fiber or electronmicroscope 12 that allows optical access to or other ability to imagethe sample 50. Three fine-threaded adjustment screws 14 enable coarselateral adjustment of the sample. Prior to tunneling, the tip-samplejunction is coarsely aligned to the region of interest with theassistance of the fiber or electron microscope and the three adjustmentscrews. The beetle-style ACSTM is equipped with three piezoelectric tubescanners (walker legs) 16 that allow fine adjustment of the tip-samplejunction. Each walker leg is patterned with four outer quadrantelectrodes and an inner electrode. By individually addressing thesequadrants, fine adjustments can be made in the sample position. Othercoarse approach and maneuvering mechanisms will also work for thislocation and are included within the scope of this invention.

[0031] The instrument is tunable over a wide frequency range and has theability to introduce up to three or more frequencies to the tunnelingjunction simultaneously. The manner by which an AC signal of multiplefrequencies may be formed and applied in ACSTM is described in U.S. Pat.No. 5,581,193, which is incorporated herein in its entirety byreference. The instrument detection system is capable of detectingtransmitted and reflected, fundamental and nonlinear alternating currentsignals, and can determine phase as well as magnitude information.Details of such capability are described in U.S. Pat. Nos. 5,268,573 and5,281,814, which are incorporated herein in their entireties byreference. This allows us local access to the frequency dependence,energy, and position of electronic responses of doped semiconductors.Introducing multiple frequencies to the STM probe tip allows us togenerate a difference frequency signal that is produced due to thenonlinear nature of the STM tunnel junction. The applicants have alreadyused this method to probe the electronic properties of self-assembledmonolayers and single molecules. The present invention extends thetechnique to semiconductor dopant profiling.

[0032] As shown below, the nonlinear AC signal is sensitive to dopanttype and density, giving us a convenient means to integrate a dopantprofiling system with the high-resolution STM. In this application, theapplicants first characterize the frequency and voltage response of thetechnique, and then use it to image patterns on doped semiconductorsubstrates to determine both dopant density and dopant type.

[0033] Data acquisition was accomplished using a difference frequencymixing strategy. A schematic of the instrument configuration 20 is shownin FIGS. 2A, 2B. In addition to the conventional DC bias applied to thetunnel junction through tip 22 by means of an adjustable DC source 24,AC signals at two frequencies ω₁ and ω₂ are introduced from a tunablewaveform generator 30 that includes sources 32, 34 providing AC signalsat two frequencies ω₁ and ω₂ respectively. An external reference 36provides a reference carrier frequency. The two sources modulate suchcarrier signal at two frequencies ω₁ and ω₂ to provide two AC signals,and combiner 38 combines the two AC signals from the sources. Themodulation frequencies ω₁ and ω₂ are offset by a small amount (typically5 kHz) that becomes the detected frequency (ω₁−ω₂=Δω). The mixingproduct (Δω) occurs at low frequency, so it is conveniently extractedand detected using a lock-in amplifier 40. Other test equipment such asnetwork analyzers, spectrum analyzers, and bandpass filters can be usedfor detection instead of a lock-in amplifier and are included within thescope of this invention. A reference signal Δω_(ref) for the lock-in iscreated by splitting off a portion of the applied AC signals prior tothe tunnel junction in a directional coupler 42, and sending themthrough a diode 44 to generate the desired difference frequency. Manyother possible nonlinear elements 44 can be used for this purpose andare included within the scope of this invention. The applied AC signalscontaining the two modulation frequencies ω₁ and ω₂ are coupled to thetip 22 by means of bias tee 46. Other means of coupling AC and DCsignals are possible, and are included within the scope of thisinvention. Where the AC signal applied contains components of three ormore frequencies, the lock-in amplifier may be set to amplify at adifference frequency substantially equal to the difference between thefrequencies of any pair of frequency components in the signal, or aninteger multiple thereof. More than one lock-in amplifier or otherdetector may also be employed to detect at more than one differencefrequency; such and other variations are within the scope of theinvention.

[0034] Thus, two frequencies, ω₁ and ω₂ are generated and combined bycombiner 38. A portion of the mixed signal is sent through a non-linearelement such as a diode 44, which creates the nonlinear differencefrequency reference signal, Δω_(ref) for the lock-in amplifier or otherdetector. The remainder of the mixed signal is combined with the DC biasvoltage and sent to the STM tip 22. The nonlinear nature of the STMtunnel junction and of the sample creates the difference frequencysignal, Δω_(signal). This is extracted from the tunnel current and sentto the lock-in amplifier or other detector for comparison with Δω_(ref).

[0035] The sources 32, 34 are tunable, so that the two frequencies ω₁and ω₂ may be swept from 0 to about 20 GHz or higher, or from a high tolow frequency (e.g. 20-0 GHz). Each of the sources may comprise, forexample, a microwave oscillator controlled by an analyzer, to tune thefrequency of its output. The tuning of the frequencies ω₁ and ω₂, anddetection by amplifier 40, may be controlled by computer 54.Alternatively, where it is not necessary to find optimum values of thetwo frequencies ω₁ and ω₂, or where this has already been accomplished,sources 32, 34 could be fixed frequencies sources, or be operated atfixed frequencies.

[0036] The tip-sample distance is precisely controlled using the DCtunneling current for feedback from amplifier 48, preventing the metaltip from contacting the semiconductor substrate 50. Such distance iscontrolled by means of control electronics 52 under the control ofcomputer 54. Using the tunneling current for controlling the tip-sampledistance, it is possible to maintain a smaller, more stable separationbetween tip and sample. This ultimately yields higher resolution thantechniques such as scanning capacitance microscopy. It is also possibleto use the force exerted on the tip 22 by the sample 50 for controllingthe tip-sample distance in an arrangement often used in atomic forcemicroscopy. One example of such tip-sample distance control is describedin the article by J. Schmidt et al. referenced above. This alternativemethod of tip-sample distance control enables a wider range of materialsto be probed.

[0037] This tip-air-semiconductor or tip-vacuum-semiconductorarrangement resembles a metal-insulator-semiconductor (MIS) structure.Also, the semiconductor surface is often passivated with a thininsulating layer (oxide or other). Signals resulting from an MISstructure will consist of both capacitive C(V) and conductive G(V)terms. C(V) originates from the capacitances of the air (or vacuum) gapand semiconductor depletion layer. Thus, the application of a positiveelectrical potential to tip 22 attracts more electrons towards thesurface of substrate 50, thereby increasing the capacitance C(V). G(V)describes losses in the AC signal from effects such as the STM tunnelingcurrent, series resistance in the semiconductor substrate, and sampleand tip local density of states.

[0038] The difference frequency detection strategy makes use of thecapacitive characteristics of the doped semiconductor, which varyaccording to dopant density and type. Additionally, it allows us to tunethe instrument over a range of fundamental frequencies, in a range ofabout 0-20 GHz, while the output signal detected by amplifier 40 remainsat a constant frequency. One expects the difference frequency signal tobe analogous to the sum frequency signal, and be proportional to dC/dV.The capacitive part of the AC output signal i at frequency ω can bewritten in the form of a Taylor series expansion: $\begin{matrix}{{\underset{\_}{i} = {{{j\omega}\left( {{C\left( V_{0} \right)} + {\frac{\delta \quad C}{\delta \quad V}{_{V_{0}}{\underset{\_}{v} + {\frac{1}{2}\frac{\delta^{2}C}{\delta \quad V^{2}}}}}_{V_{0}}{\underset{\_}{v}}^{2}} + \ldots}\quad \right)}\underset{\_}{v}}},} & \left. 1 \right)\end{matrix}$

[0039] where V₀ is the dc bias voltage, C(V) is the capacitance, V thevoltage applied and v=vexp(jωt) t), where t is time. For two ac inputsignals, v₁=Vcos(ω₁t) and v₂=Vcos(ω₂t), Eq. (1) can be expanded to yieldthe component of the difference frequency (ω₁−ω₂)as part of the totaloutput current, i_(tot): $\begin{matrix}{{{i_{tot} = {\ldots + {\frac{1}{2}\frac{\delta \quad C}{\delta \quad V}}}}}_{V_{0}}\left( {\omega_{1} - \omega_{2}} \right)V^{2}{\cos \left( {\left\lbrack {\omega_{1} - \omega_{2}} \right\rbrack t} \right)}\quad {\ldots \quad.}} & \left. 2 \right)\end{matrix}$

[0040] Eq. (2) shows that the difference frequency is proportional tothe first derivative of the capacitance. Because the capacitivecharacteristics of n- and p-type Si are different, the differencefrequency should provide an effective contrast mechanism for profilingdopants. A more complete discussion of mixing signals andcharacteristics of doped Si can be found in Schmidt et al. referencedabove and High Resolution Dopant Profiling Using a Tunable AC ScanningTunneling Microscope, G. S. McCarty, Z. J. Donhauser, L. A. Bumm, and P.S. Weiss, Characterization and Metrology for ULSI Technology: 2000International Conference, D. G. Seiler, A. C. Diebold, T. J. Shaffner,R. McDonald, W. M. Bullis, P. J. Smith, and E. M. Secula, editors(American Institute of Physics, New York, 2001), 641.

[0041] For the initial characterization experiments on uniformly dopedSi, the applicants purchased p- and n-type silicon samples from VirginiaSemiconductors, Inc, Fredericksburg Va. 22401. Samples were prepared byannealing at 950° C. for one hour, and then the surfaces were cleanedwith a 1:1 H₂O₂:HCl solution.

[0042] To fabricate patterned substrates, the applicantsphotolithographically prepared a stripe pattern with a 2 μm pitch. Bothboron-doped p-type and phosphorus-doped n-type bulk silicon withconcentrations of 1×10¹⁵ cm⁻³ were used as the base substrates. Theapplicants implanted both n- and p-type bulk substrates with boron dosesranging from 1×10¹¹ cm⁻² to 2×10¹⁴ cm⁻² or phosphorus doses ranging from1×10¹¹ cm⁻² to 3×10¹⁴ cm⁻². All boron implants were done at 35 keV andall phosphorus implants were done at 50 keV. The samples discussed beloware bulk n-type Si doped with a 1×10¹¹ cm⁻² dose of boron, and bulkp-type Si doped with a 2×10¹³ cm⁻² dose of boron. The final samplesconsisted of implanted 0.5 μm stripes spaced by 1.5 μm of unimplantedsubstrate. The applicants then activated all implants by rapid thermalannealing at 1040° C. for 40 seconds.

[0043] Immediately prior to all measurements with the ACSTM, theapplicants dipped the test samples in a 48% HF solution for ˜2 minutesto remove the surface oxide. The experiments were performed in acustom-built tunable ACSTM, which has been previously described(9-11,16). All measurements were carried out at ambient temperatures andpressures.

[0044] The cleaned, doped Si substrates were used to map out thefrequency and voltage response as a function of dopant type andconcentration. In FIGS. 3A, 3B, the magnitude of the differencefrequency signal is plotted as a function of applied frequency andvoltage, for both p- and n-type Si. The difference frequency signal isstrongly dependent on the fundamental frequency.

[0045]FIG. 3A is a graphical plot of difference frequency signalmagnitude for Si(100) as a function of fundamental modulation frequencyand DC bias for 0.001 ohm-cm boron-doped silicon. A wide peak iscentered at −0.7 V sample bias.

[0046]FIG. 3B is a graphical plot of difference frequency signalmagnitude for Si(100) as a function of fundamental modulation frequencyand DC bias for 1-3 ohm-cm phosphorus-doped silicon. FIG. 3B shows datafor lightly doped n-type Si (1-3 Ω-cm phosphorous-doped). The peak forphosphorous doping occurs close to 0 V bias. For both n- and p-type Si,relatively low applied frequencies provide the largest signals. This canbe attributed to attenuation of high frequency signals through thetransmission lines leading into the ACSTM. Reflections of the highfrequency signals can occur at transmission line connectors and incoupling to the STM tip. This results in further loss at high frequency,and less signal generated in the tunnel junction for frequencies greaterthan several hundred MHz. Fortunately, a large nonlinear effect is seenat low frequencies providing the difference frequency signal necessaryfor semiconductor characterization. It is important to note that thedata displayed in this figure is the magnitude of the differencefrequency signal; all phase information has been neglected. Becausechanges in tip size and shape as well as the precise sample orientationcan affect the phase of the difference frequency signal, between the n-and p-type Si it can be difficult to compare phase information. Asdescribed below, a phase difference when n- and p-type Si are comparedon the same substrate is expected.

[0047]FIG. 4A is a graphical plot of model capacitance curves of ametal-insulator-semiconductor structure for both a p- and an n-typesemiconductor to illustrate the invention. FIG. 4B is a graphical plotof corresponding dC/dV curves to those in FIG. 4A, determinednumerically based on the capacitance curves in FIG. 4A.

[0048] If one considers the ACSTM tip-gap-semiconductor as a MISstructure, the precise shape and magnitude of these curves would bedetermined by a variety of factors, including the dopant concentration,the distance of the tip from the sample (the insulator thickness), themagnitude of the tunneling current, and the probe tip geometry. Althoughthey only model the system of the invention of this application, thecurves in FIGS. 4A, 4B may be used to understand qualitatively thedifference frequency signal observed in images at different biases.Because one expects the magnitude and phase of the signal to be relatedto the differential capacitance, one expects that the largest signalswould occur at bias voltages near 0 volts, as illustrated in FIGS. 4A,4B, and that the signal would decrease as the magnitude of the biasincreases. Additionally, one expects an 180° relative phase shiftbetween n- and p-type regions on the semiconductor surface, asillustrated in FIG. 4B. Voltage offsets can occur from the specificsurface treatment, band bending, and other effects. While the tunableACSTM system is significantly more complicated than a simplefixed-geometry MIS capacitor, the dC/dV model is a first-orderapproximation for the contrast observed in difference frequency imagesobtained at different bias voltages. Thus, the difference frequencysignal signature as shown in FIG. 4B may be used to compare with thatobtained from a sample with unknown dopant type to determine the type(e.g. n- or p-) of dopants in the sample.

[0049] A series of bias dependent images demonstrate the trendsdescribed above. FIGS. 5A-5D are difference frequency images of ann-type substrate doped with boron. The sample was prepared to have 0.5μm p-type (with a nominal concentration of 10¹⁵ cm⁻³) stripes, with abackground of 1.5 μm n-type stripes (10¹⁵ cm⁻³). After locating thepattern, difference frequency images were acquired at voltages rangingfrom −1.5 V to +1.5 V. There is a strong bias dependence observed in thedifference frequency images. Between all of the images, the largestsignals are seen at +0.5 V and −0.5 V. This is expected for values nearzero, based on the model differential capacitance curves. The stripefeature is still evident at higher bias voltages, but the magnitude ofthe difference frequency signal has greatly diminished. The expected180° phase shift between n- and p-type silicon is observed in the imagesacquired at high voltage, confirming the assignment of the differentregions. FIGS. 5A-5D are 1.2 μm×1.2 μm difference frequency images of a1×10¹⁵ cm⁻³ boron implant stripe in a 1×10¹⁵ cm⁻³ phosphorus-dopedSi(100) substrate at varying biases. The implant stripes were definedphotolithographically to have a width of 0.5 μm. Correspondingtopographic images are inset. The vertical bars indicate signalmagnitude. The applicants have also demonstrated the ability of theACSTM to distinguish between areas of differing dopant concentration forthe same dopant type.

[0050]FIG. 6 is a 1.2 μm×1.2 μm difference frequency image of a 10¹⁵cm⁻³ p-type Si(100) substrate nominally doped with stripes of 10¹⁸ cm⁻³boron. Again, the area of higher concentration was implanted as 0.5 μmwide stripes with a pitch of 2 μm defined photolithographically. Thecorresponding topographic image is inset. In this case, the stripefeature is completely absent from the inset topographic image, yet showsup clearly in the corresponding difference frequency image. From theseand related results, one ascertains that the magnitude of the differencefrequency signal depends strongly on the local dopant density, and notsolely on dopant type. The results also demonstrate the ability of theACSTM to differentiate between areas of high and low concentration ofthe same dopant type using difference frequency detection. Thiscapability is important for imaging patterned substrates and devices.

[0051] From FIGS. 3A, 3B, and 4B, it is evident that the differencesignal frequency amplitude depends on the DC bias applied. As notedabove, even though the difference signal frequency amplitude is expectedto be maximum at around zero volts DC sample bias, this may not be thecase; in FIG. 3A, for example, such amplitude is maximum at about −0.7volts. Therefore, for optimal results, it is desirable to vary the DCsample bias applied by source 24 until the difference signal frequencyamplitude or the contrast between doped regions is optimal. For someapplications, this may mean that the DC voltage should be varied untilthe difference signal frequency amplitude is maximum. For otherapplications, such as where it is desirable to find the location of ap-n junction, for example, the maximum contrast between the differencesignal frequency amplitude detected in the p-region as opposed to thatdetected in the n-region is of greater interest. For this purpose, theDC bias of source 24 may be varied until such contrast is maximized,such as by maximizing the difference between the amplitude of thedifference frequency signal detected at the n-region and that detectedat the p-region. Patterns may be mapped optimally by comparingdifference frequency images recorded at two or more DC sample biases.This and related comparisons of multiple images are within the scope ofthe invention.

[0052] Instead of detecting at a difference frequency, the lock-inamplifier 40 or other type of detector may be set to detect a multiple(such as an integral multiple) of the difference between the frequenciesof two signal components in the AC signal applied to the tip 22 duringthe above-described optimization process and subsequent measurementprocess.

[0053] As is also evident from FIGS. 3A, 3B, the magnitude of thedifference frequency signal also depends strongly on the fundamentalmodulation frequencies applied by AC signal sources such as sources 32and 34 to modulate the reference frequency of the external reference 36.Thus, under the control of computer 54 (connection not shown in FIG.2A), the modulation frequencies applied by sources 32, 34 may also bevaried to optimize the magnitude of the difference frequency signalsdetected by the amplifier 40 or the magnitude at a frequency equal to amultiple of the difference frequency. During such process, computer 54preferably controls the sources, such as 32, 34, so that modulationfrequencies are increased or decreased by substantially the same amount,thereby allowing the lock-in amplifier 40 to detect at a constantdifference frequency or a multiple thereof. This permits system 20 todetermine the optimal modulation frequencies that should be generated bythe sources, such as sources 32, 34, so that the magnitude of thedifference frequency (or an integer multiple thereof) signal isoptimized.

[0054]FIG. 2A is a block diagram illustrating a portion of system 20 ofFIG. 2A where a moving stage 60 supports sample 50 and is used to causerelative motion between sample 50 and the STM tip 22 in a plane (such ashorizontal XY plane) that is substantially perpendicular to thedirection of movement (such as in a vertical Z direction) of tip 22, sothat tip 22 can be caused to scan over an area in the plane of sample50. This permits dopant profiles such as those shown in FIGS. 5A-5D and6 to be generated.

[0055] From experiments performed, the applicants found that wheresemiconductors are doped by the same dopants but to different dosages,densities or concentrations, that at the DC sample biases most commonlyemployed, the lightly doped regions of the sample would cause a highermagnitude difference frequency signal than an area doped at a higherconcentration, and that the magnitude of the difference frequency signaldepends strongly and monotonically on the dopant density orconcentration. This is illustrated in FIG. 7. Thus, since theresistivity of a doped semiconductor varies inversely and monotonicallywith dopant density, from FIG. 7 it is evident that the differencefrequency signal amplitude also varies inversely and monotonically withdopant density. This allows actual dopant density or concentration to bedetermined using a reference, such as a reference database.

[0056] Thus, reference samples with known dopant dosages, densities orconcentrations may be measured using system 20 of FIGS. 2A, 2B toprovide reference data, such as in the form of graphs of the type shownin FIG. 7. This may be repeated with different dopants (e.g. boron,phosphorus, etc.) at different dopant densities to compile differentsets of reference data. Then when it is desirable to determine thedopant density of a particular sample, first the dopant type isdetermined. Thus, n- and p-dopant types may be differentiated bymeasuring the change in the difference signal frequency as the DC biasis varied, as illustrated in FIG. 4B. The particular dopant (such asboron or phosphorus) may be determined by comparison to the differentsets of reference data obtained. The dopant dosages, densities orconcentrations may then be obtained by comparison of the differencefrequency signal measured, in some cases as a function of DC sample biasvoltage, or at one or more DC sample bias voltages, compared to thereference data measured from samples of known dosages, densities orconcentrations of the same dopant. Where the reference data are obtainedfrom reference samples of known dopant densities in the form of graphsshown in FIG. 7, a comparison of the difference frequency signalamplitude measured with the reference graph will yield the resistivityof the sample measured. The dopant density can then be obtained fromsuch resistivity by calculation, or by referring to available datarelating dopant density to resistivity of doped semiconductor materials.

[0057] As shown in FIG. 2A, the difference frequency signal measured byamplifier 40 is supplied to computer 54 for compiling the reference datasets and for performing the comparison between data measured from asample of a known dopant or dopant concentration to reference datastored in computer 54. Computer 54, in turn, controls lock-in amplifier40 so that amplifier would detect at a difference frequency or amultiple thereof.

[0058] Where it is desirable to provide an image of a sample substratedoped in various regions, a difference frequency image of the sample maybe adequate to determine the locations of the doped regions, such asillustrated in FIGS. 5A, 5B and 6.

[0059]FIG. 8A is a topograhical image of a doped semiconductor sample,and FIG. 8B is a profile of the sample obtained using the invention ofthe difference frequency signal amplitude. As is evident from acomparison of FIGS. 8A, 8B, the invention is capable of measuring singleatomic vacancies that function as dopants.

[0060] While the invention has been described above by reference tovarious embodiments, it will be understood that changes andmodifications may be made without departing from the scope of theinvention, which is to be defined only by the appended claims and theirequivalent. All references referred to herein are incorporated byreference in their entireties.

What is claimed is:
 1. A method for measuring dopants in semiconductors,comprising: applying an AC electrical signal to a semiconductor sample,said signal including at least two frequency components; detecting asignal at the sample at a detection frequency substantially equal to thefrequency difference between the at least two frequency components or amultiple thereof; and processing the signal detected to measure dopantsin the sample.
 2. The method of claim 1, further comprising applying aDC bias voltage across an electrode and the sample.
 3. The method ofclaim 2, further comprising altering amplitude of the DC bias voltageuntil the signal detected is optimized.
 4. The method of claim 3,wherein amplitude of the DC bias voltage is altered until the signaldetected is maximized in amplitude.
 5. The method of claim 3, whereinamplitude of the DC bias voltage is altered until contrast betweensignals detected at said detection frequency as a result of dopantshaving two different responses to the AC signal in the sample ismaximized.
 6. The method of claim 1, wherein the processingdistinguishes between p and n type dopants.
 7. The method of claim 6,wherein the applying applies the AC signal by means of an electrode,said method further comprising applying a DC bias voltage across theelectrode and the sample, and altering amplitude of the DC bias voltageuntil the signal detected is optimized so that said detecting detectsthe signal at said detection frequency when the signal detected isoptimized.
 8. The method of claim 1, wherein the applying applies the ACsignal by means of an electrode, said method further comprising scanningthe electrode across a surface of the sample wherein the processingprovides a dopant profile of the sample.
 9. The method of claim 8, saidmethod further comprising applying a DC bias voltage across theelectrode and the sample, and altering amplitude of the DC bias voltageuntil the signal detected is optimized so that said detecting detectsthe signal at said detection frequency when the signal detected isoptimized.
 10. The method of claim 8, wherein the processing comparesthe detected signal to reference data to determine a profile of type ofdopants or a profile of dosage or density of dopants in the sample. 11.The method of claim 1, further comprising measuring samples with knowndosage or density of dopants to obtain the reference data.
 12. Themethod of claim 1, wherein the processing compares the detected signalto reference data to determine dosage or a parameter related to densityof dopants in the sample.
 13. The method of claim 12, further comprisingmeasuring samples with known dosage or density of dopants to obtain thereference data.
 14. The method of claim 1, wherein said applying appliesthe signal so that frequencies of said at least two frequency componentschange.
 15. The method of claim 14, wherein said applying applies thesignal so that frequencies of said at least two frequency componentsincrease or decrease by substantially the same amount when saiddetecting detects at said detection frequency.
 16. An apparatus formeasuring dopants in semiconductors, comprising: a source supplying anAC electrical signal to a semiconductor sample, said signal including atleast two frequency components; a detector detecting a signal at thesample at a detection frequency substantially equal to the frequencydifference between the at least two frequency components or a multiplethereof; and a processor processing the signal detected using predictedor reference data for dopants to measure dopants in the sample.
 17. Theapparatus of claim 16, further comprising a database containingreference data on dopants.
 18. The apparatus of claim 16, wherein theprocessor compares the signal detected to predicted data to distinguishbetween p and n type dopants.
 19. The apparatus of claim 16, furthercomprising an electrode, wherein the source applying applies the ACsignal by means of an electrode, said apparatus further comprising aninstrument causing relative motion between the electrode and the sample,so that the electrode passes across a surface of the sample wherein theprocessor provides a dopant profile of the sample.
 20. The apparatus ofclaim 19, wherein the processing compares the detected signal toreference data to determine a profile of type of dopants or a profile ofdosage or density of dopants in the sample.
 21. The apparatus of claim16, further comprising a database containing reference data on dopants,wherein the processor compares the detected signal to the reference datato determine dosage or density of dopants in the sample.
 22. Theapparatus of claim 16, further comprising an electrode, wherein thesource applies the AC signal by means of an electrode, said apparatusfurther comprising an instrument aligning the sample with the electrode.23. The apparatus of claim 22, said instrument comprising an opticaland/or electron microscope providing a signal to the sample andadjustment screws for lateral positioning of the sample relative to theelectrode.
 24. The apparatus of claim 16, further comprising anelectrode, wherein the source applying applies the AC signal by means ofan electrode, said apparatus further comprising a second source applyinga DC bias voltage across the electrode and the sample.
 25. The apparatusof claim 24, wherein said second source is tunable to apply a DC biasvoltage of variable amplitude to optimize the signal detected.
 26. Theapparatus of claim 16, wherein said source is tunable so thatfrequencies of said at least two frequency components are increased ordecreased by substantially the same amount when said detector detects atsaid detection frequency.